Fireworks' sublayers are definitely problematic. I avoid them. That said, this is one area where the sublayer system seems to work just fine. When using the Duplicate Layer function, it's OK that the sublayers and their content don't appear to be selected; they're still copied when you drag the containing layer to the Duplicate Layer icon.

At least that's how it works on my system: Fireworks CS6 on Mac OS 10.6.8. (What version of Fireworks are you using and on what operating system?)

If you work with sublayers a lot, you might be interested in developer Aaron Beall's Layers Commands extension, which includes commands like "Select Entire Layer and Sublayers" and "Explode Sublayer".

That's a shame. Maybe selecting the items on the canvas might be easier?

This gets to what bugs me most about sublayers: You'd think that selecting a layer would select its contents—all of its contents. You know how layers are independent from one another? Well, sublayers pretty much act just like regular layers in that sense. All I can think is that Adobe must have added the sublayer feature in haste, to help support Photoshop compatibility, and then left it at that.

In any case, I'm surprised that the Duplicate Layer function is letting you down here; hopefully, you'll stumble onto what's causing the problem or else find a decent workaround.

I rarely use sublayers, so I didn't notice that selecting a layer doesn't also select all the elements in its sublayers. That's obviously stupid, but Aaron's command is a workaround that you could assign to a keyboard shortcut to quickly select everything.

When I want things to move together, I use groups, and often groups within groups. You can't see the contents of a group in the Layers panel, sadly, but you can sub-select elements in the group directly on the canvas. If you do want to see inside a group, Aaron has a panel for that: http://fireworks.abeall.com/extensions/panels/#Object